Probing soap-film friction with two-phase foam flow

Abstract

We have created a novel, stable pattern of quasi-two-dimensional (2D) foam flow that enables us to measure the relationship between the drag force on a soap-film sliding on a glass plate and the drag force on a soap-film sliding on another soap-film. We created a flowing homogenous 2D foam by supplying bubbles at a steady rate into one end of a Hele–Shaw cell. Part of the way along the midline of the cell, we injected air through the upper plate, inflating bubbles as they flowed by. These bubbles formed a constant-width band along the midline of the cell that moved with the background flow at low injection rates and faster than the background flow at higher injection rates. Fitting our experimental data to a simple theoretical model based on linear drag and minimization of frictional dissipation, we show that the drag force from the wetting layer on the glass plates is an order of magnitude smaller than the drag from other soap-films.

Keywords:

• bubbles
• films
• fluids
• foams
• friction

Acknowledgments

Rebecca Perry participated in this project as an NSF-funded REU student at Indiana University during the summer of 2006. Ms Perry received her BS from Bowdoin College in May 2007. J.A. Glazier is grateful for the inspiration, support and hospitality of the late Prof. Manuel Fortes, Prof. Fatima Vaz, Prof. Emilia Rosa, and the Fortes group at the Instituto Superior Tecnico, Lisbon, Portugal during annual spring visits over a period of many years.

We acknowledge support from National Institutes of Health, National Institute of General Medical Sciences, grants 1R01 GM076692-01 and 1R01 GM077138-01A1, and the College of Arts and Sciences, the Office of the Vice President for Research and the Biocomplexity Institute, all at Indiana University, Bloomington.

Notes

Notes

1. Research Experience for Undergraduates, an NSF-funded program.

2. Intermittently, instead of a single soap-film, a cord of small bubbles would span the channel. We excluded these events from our analysis.

3. At the low flow rates in our experiments, the increase in bubble size due to the pressure drop, from the end where foam entered the flow-cell to the end where it left, was insignificant.

4. Variational principles for dissipative non-equilibrium systems have a long history, starting with Rayleigh's dissipation function. They were further developed by Onsager and Prigogine, and continue to be an active area of research.

5. Foam-drainage experiments have shown that different surfactants can create a range of boundary conditions to fluid flow in Plateau borders, from free-slip (leading to a “plug” profile) to no-slip (leading to a Poiseuille profile) 10.